Simulations of the evolution of a relativistic electron beam injected into the Earth's magnetosphere are examined. It is found that the lifetime of beam particles strongly depends on the initial pitch angle distribution and that lifetimes similar to those found for the radiation belts are obtained for nearly equatorially mirroring injections. It is concluded that the results of our previous study on beam propagation [Khazanov et al., 1999>, which only considered upper ionospheric injections, are consistent with other relativistic electron studies and should be regarded as an examination of the loss cone edge population, whether naturally occurring or artificially injected into near-Earth space.